I have a DC500, the model prior to DC600 but very similar. When the DC500 first came out, the std battery was 650 mAh and it would barely last a dive. About a year ago I was able to get a 750 mAh battery from Pioneer (the manufaturer). It lasts 1-2 dives pretty well. I use the external strobe and set the camera to go to sleep after 30 seconds and turn off after 5 minutes.
I believe that the DC600 comes with the 750 mAh battery. Make sure that you have that battery. It should last for two dives, but I change mine after every dive just in case. I shoot a good bit of video with mine so that eats battery.
I now carry three batteries plus the charger unit that goes on the power supply. I do a lot of liveaboards, so I can always have a fresh battery and one in the charger.
If you have problems, call Pioneer directly. I have and have become my LDS's expert on all things DC500/600.
PM me if you want any further info.